SOLUTION: If U= {1,2,3,4,5,6,7,8}, A= {2,4,6,4,8} and n(AxB')=24 find number of subsets of B Thanks!

Algebra ->  Subset -> SOLUTION: If U= {1,2,3,4,5,6,7,8}, A= {2,4,6,4,8} and n(AxB')=24 find number of subsets of B Thanks!      Log On


   

Question 906030: If U= {1,2,3,4,5,6,7,8}, A= {2,4,6,4,8} and n(AxB')=24 find number of subsets of B

Thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
As a rule, if n(A) = k and n(B) = m, then

n(A x B) = k*m

The terms k and m are positive whole numbers. We're given A= {2,4,6,4,8} which means set A has 5 elements. In other words, n(A) = 5.

So

n(A x B') = 5*n

where n is the number of elements in set B'. There's a problem though: if 5*n were equal to 24, then n is NOT a whole number since 5*n = 24 --> n = 24/5 = 4.8

So there is no possible way that there are 5 elements in set A. Set A needs to have either 1, 2, 3, 4, 6, 8, 12, or 24 elements. Notice how I listed the factors of 24.

This all leads me to think there is a typo somewhere.